Question

possible answers

abcd ≅ efgh

scale factor is 2:1

corresponding sides are proportional

a dilation maps △abcd onto △efgh

scale factor is 1:1

corresponding sides are congruent

abcd ~ efgh

a translation maps △abcd onto △efgh

congruent

no answers chosen

similar

no answers chosen

Explanation:

Step1: Analyze congruent figures

Congruent figures have the same shape and size. For the first pair of figures (top - two quadrilaterals), all corresponding sides and angles are equal. The scale factor \(1:1\) (since \(\frac{3}{3}=\frac{2}{2}=\frac{6}{6}=\frac{7}{7} = 1\)) implies that corresponding sides are congruent. A translation (a type of rigid transformation) can map one figure onto the other as rigid transformations preserve side - lengths and angles. So, \(ABCD\cong EFGH\).

Step2: Analyze similar figures

Similar figures have the same shape but not necessarily the same size. For the second pair of figures (bottom - two quadrilaterals), check the ratios of corresponding sides. \(\frac{10}{5}=\frac{8}{4}=\frac{14}{7}=\frac{16}{8}=2\). Since the ratios of corresponding sides are equal (corresponding sides are proportional), by the definition of similar polygons (if the ratios of all corresponding sides are equal and corresponding angles are equal), \(ABCD\sim EFGH\). A dilation (a non - rigid transformation that changes the size but not the shape) can map one figure onto the other as it changes the size of the figure while keeping the shape (angle measures and the ratio of side - lengths) the same.

Answer:

• For congruent: \(ABCD\cong EFGH\), scale factor is \(1:1\), corresponding sides are congruent, a translation maps \(ABCD\) onto \(EFGH\).
• For similar: \(ABCD\sim EFGH\), corresponding sides are proportional, a dilation maps \(ABCD\) onto \(EFGH\).